Finite Group Databasebeta

← C47×#29744 #26069442

Subgroups — C47×#29744 #26069442

Order 12032.

1168 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#407C211yesmaximal, characteristic, complemented
3C47×#2848C211yesmaximal, characteristic, complemented
4C47×#2847C211yesmaximal, characteristic
5C47×#2076C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2036C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#2000C211yesmaximal, characteristic, complemented
12C47×#2000C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1894C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic, complemented
18C22×M16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#120×C47—21no—
27C47×#468—24no—
28C2×#107×C47C2211yescharacteristic, complemented
29C2×#107×C47C2211yescharacteristic, complemented
30C2×#106×C47C2211yescharacteristic, complemented
31C2×#103×C47C2211yescharacteristic, complemented
32C2×#103×C47C2211yescharacteristic, complemented
33C2×#103×C47C2211yescharacteristic, complemented
34C2×#102×C47C2211yescharacteristic, complemented
35C2×#102×C47C2211yescharacteristic, complemented
36C2×#102×C47C2211yescharacteristic, complemented
37C47×#407—24no—
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2211yescharacteristic
42C47×#386—21no—
43C47×#386—21no—
44C47×#386—21no—
45C47×#385—21no—
46C47×#385—21no—
47C47×#385—21no—
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#380C2211yescharacteristic
54C47×#379—21no—
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C25×C47D411yescharacteristic
62C22×Q8×C47C2311yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—22no—
68C23×C4×C47—22no—
69C23×C4×C47—41no—
70C23×C4×C47—41no—
71C23×C4×C47—41no—
72C23×C4×C47—41no—
73C23×C4×C47D411yescharacteristic
74C23×C4×C47D411yescharacteristic
75C23×C4×C47D411yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—41no—
81C2×SD16×C47—41no—
82C2×M16×C47—22no—
83C2×M16×C47—41no—
84C2×M16×C47—41no—
85C2×M16×C47—41no—
86C2×M16×C47—41no—
87C2×M16×C47D414yescomplemented
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—41no—
95C22⋊Q8×C47—41no—
96C22⋊Q8×C47—41no—
97C22⋊Q8×C47—41no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—41no—
101#121×C47—41no—
102#121×C47—41no—
103#121×C47—41no—
104#120×C47—44no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126#107×C47—22no—
127#107×C47—41no—
128#106×C47—41no—
129#103×C47—22no—
130#103×C47—41no—
131#103×C47—41no—
132#102×C47—22no—
133#102×C47—41no—
134#102×C47—41no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—22no—
137C22⋊C8×C47—22no—
138C22⋊C8×C47—22no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—21no—
149C24×C47—41no—
150C24×C47—41no—
151C24×C47—41no—
152C24×C47—41no—
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
155C24×C47C2×D411yescharacteristic
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—42no—
174C2×D4×C47—42no—
175C2×D4×C47—42no—
176C2×D4×C47—42no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—41no—
204C22×C4×C47—41no—
205C22×C4×C47—41no—
206C22×C4×C47—41no—
207C22×C4×C47—41no—
208C22×C4×C47—41no—
209C22×C4×C47—44no—
210C22×C4×C47—44no—
211C22×C4×C47—44no—
212C22×C4×C47—44no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47#4112yes—
218C22×C4×C47C2411yescharacteristic
219SD16×C47—44no—
220M16×C47—44no—
221M16×C47—44no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47C2×D412yes—
233C2×C8×C47C2×D412yes—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—42no—
247C4⋊C4×C47—42no—
248C4⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—44no—
280C23×C47—44no—
281C23×C47—44no—
282C23×C47—44no—
283C23×C47—44no—
284C23×C47—44no—
285C23×C47—44no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47#12112yes—
294C23×C47AGL(1,ℤ/8)12yes—
295C23×C47#13712yes—
296C23×C47C22×D411yescharacteristic
297Q8×C47—41no—
298Q8×C47—41no—
299Q8×C47—41no—
300Q8×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—84no—
306D4×C47—84no—
307D4×C47—84no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—44no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47#12112yes—
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C2×#4111yescharacteristic
355C2×C4×C47H(5,𝔽2)11yescharacteristic
356C2×C4×C47H(5,𝔽2)11yescharacteristic
357C2×C4×C47H(5,𝔽2)11yescharacteristic
358C2×C4×C47H(5,𝔽2)11yescharacteristic
359C8×C47—22no—
360C8×C47—22no—
361C8×C47—41no—
362C8×C47—41no—
363#29744C4711yesmaximal, characteristic, direct product factor, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—416no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47C2×#12111yescharacteristic
394C22×C47#53411yescharacteristic
395C22×C47#53411yescharacteristic
396C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C47C2×#13711yescharacteristic
398C22×C47#57511yescharacteristic
399C22×C47#57511yescharacteristic
400C4×C47—22no—
401C4×C47—41no—
402C4×C47—41no—
403C4×C47—81no—
404C4×C47—81no—
405C4×C47—81no—
406C4×C47—81no—
407C4×C47—81no—
408C4×C47—81no—
409C4×C47—81no—
410C4×C47#53411yescharacteristic
411C4×C47#53511yescharacteristic
412C4×C47#53811yescharacteristic
413C4×C47#53811yescharacteristic
414C2×#468C2×C4711yescharacteristic, complemented
415C2×#407C2×C4711yescharacteristic, complemented
416#2848C2×C4711yescharacteristic, complemented
417#2847C2×C4711yescharacteristic
418#2076C2×C4711yescharacteristic, complemented
419#2075C2×C4711yescharacteristic, complemented
420#2036C2×C4711yescharacteristic, complemented
421#2035C2×C4711yescharacteristic, complemented
422#2034C2×C4711yescharacteristic, complemented
423#2033C2×C4711yescharacteristic, complemented
424#2000C2×C4711yescharacteristic, complemented
425#2000C2×C4711yescharacteristic, complemented
426#1895C2×C4711yescharacteristic, complemented
427#1894C2×C4711yescharacteristic, complemented
428#1809C2×C4711yescharacteristic, complemented
429C2×C47—42no—
430C2×C47—42no—
431C2×C47—42no—
432C2×C47—161no—
433C2×C47#261711yescharacteristic
434C2×C47#305511yescharacteristic
435C2×C47#305611yescharacteristic
436C2×C47#319311yescharacteristic
437C2×C47#319411yescharacteristic
438C2×C47#319611yescharacteristic
439C2×C47#319711yescharacteristic
440C24×C4C22×C4711yescharacteristic
441C22×SD16C22×C4711yescharacteristic, complemented
442C22×M16C22×C4711yescharacteristic
443C22×M16C22×C4711yescharacteristic
444C2×C22⋊Q8C22×C4711yescharacteristic
445C2×C22⋊Q8C22×C4711yescharacteristic
446C2×C22⋊Q8C22×C4711yescharacteristic
447C2×#121C22×C4711yescharacteristic
448C2×#121C22×C4711yescharacteristic
449C2×#121C22×C4711yescharacteristic
450C2×#120—21no—
451#468—24no—
452C2×#107C22×C4711yescharacteristic, complemented
453C2×#107C22×C4711yescharacteristic, complemented
454C2×#106C22×C4711yescharacteristic, complemented
455C2×#103C22×C4711yescharacteristic, complemented
456C2×#103C22×C4711yescharacteristic, complemented
457C2×#103C22×C4711yescharacteristic, complemented
458C2×#102C22×C4711yescharacteristic, complemented
459C2×#102C22×C4711yescharacteristic, complemented
460C2×#102C22×C4711yescharacteristic, complemented
461#407—24no—
462C2×C22⋊C8C22×C4711yescharacteristic
463C2×C22⋊C8C22×C4711yescharacteristic
464C2×C22⋊C8C22×C4711yescharacteristic
465C2×C22⋊C8C22×C4711yescharacteristic
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#385—21no—
471#385—21no—
472#380C22×C4711yescharacteristic
473#380C22×C4711yescharacteristic
474#380C22×C4711yescharacteristic
475#380C22×C4711yescharacteristic
476#380C22×C4711yescharacteristic
477#380C22×C4711yescharacteristic
478#379—21no—
479#340C22×C4711yescharacteristic, complemented
480#340C22×C4711yescharacteristic, complemented
481#340C22×C4711yescharacteristic, complemented
482#340C22×C4711yescharacteristic, complemented
483#340C22×C4711yescharacteristic, complemented
484#340C22×C4711yescharacteristic, complemented
485C47#2974411yescharacteristic, direct product factor, Sylow
486C25D4×C4711yescharacteristic
487C22×Q8C23×C4711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C23×C4711yescharacteristic
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—41no—
497C23×C4—41no—
498C23×C4D4×C4711yescharacteristic
499C23×C4D4×C4711yescharacteristic
500C23×C4D4×C4711yescharacteristic
501C23×C4C23×C4711yescharacteristic
502C23×C4C23×C4711yescharacteristic
503C23×C4C23×C4711yescharacteristic
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16D4×C4714yescomplemented
513C22×C8C23×C4711yescharacteristic
514C22×C8C23×C4711yescharacteristic
515C22×C8C23×C4711yescharacteristic
516C22×C8C23×C4711yescharacteristic
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—41no—
520C22⋊Q8—41no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—41no—
528#121—41no—
529#120—44no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C4⋊C4C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C4⋊C4C23×C4711yescharacteristic
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551#107—22no—
552#107—41no—
553#106—41no—
554#103—22no—
555#103—41no—
556#103—41no—
557#102—22no—
558#102—41no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—21no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—41no—
578C24C2×D4×C4711yescharacteristic
579C24C2×D4×C4711yescharacteristic
580C24C2×D4×C4711yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4C2×D4×C4711yescharacteristic
639C22×C4C2×D4×C4711yescharacteristic
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C2×D4×C4712yes—
642C22×C4#41×C4712yes—
643C22×C4C24×C4711yescharacteristic
644SD16—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8C2×D4×C4712yes—
658C2×C8C2×D4×C4712yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23#121×C4712yes—
719C23AGL(1,ℤ/8)×C4712yes—
720C23#137×C4712yes—
721C23C22×D4×C4711yescharacteristic
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4#121×C4712yes—
778C2×C4C22×D4×C4711yescharacteristic
779C2×C4C2×#41×C4711yescharacteristic
780C2×C4H(5,𝔽2)×C4711yescharacteristic
781C2×C4H(5,𝔽2)×C4711yescharacteristic
782C2×C4H(5,𝔽2)×C4711yescharacteristic
783C2×C4H(5,𝔽2)×C4711yescharacteristic
784C8—22no—
785C8—22no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C2×#121×C4711yescharacteristic
818C22C47×#53411yescharacteristic
819C22C47×#53411yescharacteristic
820C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
821C22C2×#137×C4711yescharacteristic
822C22C47×#57511yescharacteristic
823C22C47×#57511yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C47×#53411yescharacteristic
835C4C47×#53511yescharacteristic
836C4C47×#53811yescharacteristic
837C4C47×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—161no—
842C2C47×#261711yescharacteristic
843C2C47×#305511yescharacteristic
844C2C47×#305611yescharacteristic
845C2C47×#319311yescharacteristic
846C2C47×#319411yescharacteristic
847C2C47×#319611yescharacteristic
848C2C47×#319711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C47×#468C2semidirect
2. C2×C47×#407C2semidirect
3. C47×#2848C2semidirect
5. C47×#2076C2semidirect
6. C47×#2075C2semidirect
7. C47×#2036C2semidirect
8. C47×#2035C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#2000C2semidirect
12. C47×#2000C2semidirect
13. C47×#1895C2semidirect
14. C47×#1894C2semidirect
15. C47×#1809C2semidirect
17. C22×SD16×C47C22semidirect
28. C2×#107×C47C22semidirect
29. C2×#107×C47C22semidirect
30. C2×#106×C47C22semidirect
31. C2×#103×C47C22semidirect
32. C2×#103×C47C22semidirect
33. C2×#103×C47C22semidirect
34. C2×#102×C47C22semidirect
35. C2×#102×C47C22semidirect
36. C2×#102×C47C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
87. C2×M16×C47D4semidirect
363. #29744C47direct (N × H)
414. C2×#468C2×C47semidirect
415. C2×#407C2×C47semidirect
416. #2848C2×C47semidirect
418. #2076C2×C47semidirect
419. #2075C2×C47semidirect
420. #2036C2×C47semidirect
421. #2035C2×C47semidirect
422. #2034C2×C47semidirect
423. #2033C2×C47semidirect
424. #2000C2×C47semidirect
425. #2000C2×C47semidirect
426. #1895C2×C47semidirect
427. #1894C2×C47semidirect
428. #1809C2×C47semidirect
441. C22×SD16C22×C47semidirect
452. C2×#107C22×C47semidirect
453. C2×#107C22×C47semidirect
454. C2×#106C22×C47semidirect
455. C2×#103C22×C47semidirect
456. C2×#103C22×C47semidirect
457. C2×#103C22×C47semidirect
458. C2×#102C22×C47semidirect
459. C2×#102C22×C47semidirect
460. C2×#102C22×C47semidirect
479. #340C22×C47semidirect
480. #340C22×C47semidirect
481. #340C22×C47semidirect
482. #340C22×C47semidirect
483. #340C22×C47semidirect
484. #340C22×C47semidirect
485. C47#29744direct (N × H)
512. C2×M16D4×C47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C47×#4682
C2×C47×#4072
C47×#28482
C47×#28472
C47×#20762
C47×#20752
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#20002
C47×#18952
C47×#18942
C47×#18092
#2974447